Anatomy of a q-generalization of the Laguerre/Hermite Orthogonal Polynomials

Chuan-Tsung Chan; Hsiao-Fan Liu

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arXiv · 1612.09039

Anatomy of a q-generalization of the Laguerre/Hermite Orthogonal Polynomials

Chuan-Tsung Chan·Hsiao-Fan Liu

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Abstract

We study a q-generalization of the classical Laguerre/Hermite orthogonal polynomials. Explicit results include: the recursive coefficients, matrix elements of generators for the Heisenberg algebra, and the Hankel determinants. The power of quadratic relation is illustrated by comparing two ways of calculating recursive coefficients. Finally, we derive a q-deformed version of the Toda equations for both q-Laguerre/Hermite ensembles.

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BibTeX RIS

Chuan-Tsung Chan, Hsiao-Fan Liu. 2016-12-29. Anatomy of a q-generalization of the Laguerre/Hermite Orthogonal Polynomials. https://arxiv.org/abs/1612.09039

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